Direct electrical impedance tomography for nonsmooth conductivities

DOI10.3934/IPI.2011.5.531zbMath1237.78014OpenAlexW2112400896MaRDI QIDQ645836

Jennifer L. Mueller, Samuli Siltanen, Kari Astala, Lassi Päivärinta, Allan Perämäki

Publication date: 10 November 2011

Published in: Inverse Problems and Imaging (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/ipi.2011.5.531

zbMATH Keywords

inverse probleminverse conductivity problemelectrical impedance tomographynonlinear Fourier transformBeltrami equationconductivity equationcomplex geometrical optics solutionnumerical solverquasi-conformal map

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Finite difference methods applied to problems in optics and electromagnetic theory (78M20) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Quasiconformal mappings in the complex plane (30C62) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46) Geometric optics (78A05)

Related Items (10)

Electrical impedance tomography: 3D reconstructions using scattering transforms ⋮ Numerical solution of the Beltrami equation via a purely linear system ⋮ Propagation and recovery of singularities in the inverse conductivity problem ⋮ A D-Bar Algorithm with A Priori Information for 2-Dimensional Electrical Impedance Tomography ⋮ A Hybrid Segmentation and D-Bar Method for Electrical Impedance Tomography ⋮ Nonlinear Fourier analysis for discontinuous conductivities: computational results ⋮ The D-bar method for electrical impedance tomography—demystified ⋮ Convergence of a numerical solver for an \(\mathbb R\)-linear Beltrami equation ⋮ A real-time D-bar algorithm for 2-D electrical impedance tomography data ⋮ A data-driven edge-preserving D-bar method for electrical impedance tomography

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